Non-Markovian Memory Strength Bounds Quantum Process Recoverability

Generic non-Markovian quantum processes have infinitely long memory, implying an exact description that grows exponentially in complexity with observation time. Here, we present a finite memory ansatz that approximates (or recovers) the true process with errors bounded by the strength of the non-Markovian memory. The introduced memory strength is an operational quantity and depends on the way the process is probed. Remarkably, the recovery error is bounded by the smallest memory strength over all possible probing methods. This allows for an unambiguous and efficient description of non-Markovian phenomena, enabling compression and recovery techniques pivotal to near-term technologies. We highlight the implications of our results by analyzing an exactly solvable model to show that memory truncation is possible even in a highly non-Markovian regime.Comment: 8 pages, 7 pages of appendices, 5 figures. Close to the published versio

Hidden Quantum Memory: Is Memory There When Somebody Looks?

In classical physics, memoryless processes and Markovian statistics are one and the same. This is not true for quantum processes, first and foremost due to the fact that quantum measurements are invasive. Independently of measurement invasiveness, here we derive a novel distinction between classical and quantum processes, namely the possibility of hidden quantum memory. While Markovian statistics of classical processes can always be reproduced by a memoryless dynamics, our main result establishes that this is not the case in quantum mechanics: We first provide an example of quantum non-Markovianity that depends on whether or not a previous measurement is performed -- a phenomenon that is impossible for memoryless processes; we then strengthen this result by demonstrating statistics that are Markovian independent of how they are probed, but are are nonetheless still incompatible with memoryless quantum dynamics. Thus, we establish the existence of Markovian statistics that fundamentally require quantum memory for their creation.Comment: 4.5 + 8.5 pages, 3 figure

Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory

Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise from/are transmitted via interactions between a system and its environment; as such, they can be either classical or quantum in nature. From a practical standpoint, quantum processes with classical memory promise near-term applicability: they are more powerful than their memoryless counterpart, yet at the same time can be controlled over significant timeframes without being spoiled by decoherence. However, despite practical and foundational value, apart from simple two-time scenarios, the distinction between quantum and classical memory remains unexplored. We first analyse various physically-motivated candidates regarding a suitable definition for classical memory that lead to remarkably distinct phenomena in the multi-time setting. Subsequently, we systematically characterise the hierarchy of multi-time memory effects in quantum mechanics, many levels of which collapse in the two-time setting, thereby making our results genuinely multi-time phenomena.Comment: 11+5 pages, 4 figures, 57 reference

Landauer vs. Nernst: What is the True Cost of Cooling a Quantum System?

Thermodynamics connects our knowledge of the world to our capability to manipulate and thus to control it. This crucial role of control is exemplified by the third law of thermodynamics, Nernst's unattainability principle, stating that infinite resources are required to cool a system to absolute zero temperature. But what are these resources and how should they be utilised? And how does this relate to Landauer's principle that famously connects information and thermodynamics? We answer these questions by providing a framework for identifying the resources that enable the creation of pure quantum states. We show that perfect cooling is possible with Landauer energy cost given infinite time or control complexity. However, such optimal protocols require complex unitaries generated by an external work source. Restricting to unitaries that can be run solely via a heat engine, we derive a novel Carnot-Landauer limit, along with protocols for its saturation. This generalises Landauer's principle to a fully thermodynamic setting, leading to a unification with the third law and emphasising the importance of control in quantum thermodynamics.Comment: 15 pages, 4 figures, 46 pages of appendice

Removal of non-CO2 greenhouse gases by large-scale atmospheric solar photocatalysis

Large-scale atmospheric removal of greenhouse gases (GHGs) including methane, nitrous oxide and ozone-depleting halocarbons could reduce global warming more quickly than atmospheric removal of CO2. Photocatalysis of methane oxidizes it to CO2, effectively reducing its global warming potential (GWP) by at least 90%. Nitrous oxide can be reduced to nitrogen and oxygen by photocatalysis; meanwhile halocarbons can be mineralized by red-ox photocatalytic reactions to acid halides and CO2. Photocatalysis avoids the need for capture and sequestration of these atmospheric components. Here review an unusual hybrid device combining photocatalysis with carbon-free electricity with no-intermittency based on the solar updraft chimney. Then we review experimental evidence regarding photocatalytic transformations of non-CO2 GHGs. We propose to combine TiO2-photocatalysis with solar chimney power plants (SCPPs) to cleanse the atmosphere of non-CO2 GHGs. Worldwide installation of 50,000 SCPPs, each of capacity 200 MW, would generate a cumulative 34 PWh of renewable electricity by 2050, taking into account construction time. These SCPPs equipped with photocatalyst would process 1 atmospheric volume each 14–16 years, reducing or stopping the atmospheric growth rate of the non-CO2 GHGs and progressively reducing their atmospheric concentrations. Removal of methane, as compared to other GHGs, has enhanced efficacy in reducing radiative forcing because it liberates more °OH radicals to accelerate the cleaning of the troposphere. The overall reduction in non-CO2 GHG concentration would help to limit global temperature rise. By physically linking greenhouse gas removal to renewable electricity generation, the hybrid concept would avoid the moral hazard associated with most other climate engineering proposals